The dynamics of every archery arrow flight are readily observed by an archer, but are poorly understood. The largest and most easily seen perturbation is known as "fishtailing", in which the arrow may be seen to oscillate in azimuth after leaving the bow. The second largest perturbation in known as "porpoising", in which the arrow oscillates in elevation in flight. Since the fletching, or feathers, are attached in a slightly twisted helix pattern, the arrow also rolls continuously about is flight axis. Therefore as the arrow oscillates in both pitch and yaw as it rolls, the resulting flight pattern is usually a spiral path of some amplitude to the target. The skill of the archer is not only applied to aiming the arrow at the release time, but is also applied to releasing the string and nock, while avoiding application of any perturbing torques to the bow handle. All these efforts are directed towards minimizing the input perturbations to the arrow at the moment of release.
Once released, with whatever perturbations may have been applied to the arrow, the dynamics of the arrow are a very complex set of compromises. The fastest arrow, with the shortest flight time to target, will have the least error in trajectory due to gravity and wind, and the fastest reponse time to a moving target. However, the lightest arrow is the slimmest and most flexible. The inventor has found that flexing of the arrow in flight is a most significant contributor to the pitch and yaw components of the spiral flight path. The arrow is imparted with a bending moment in pitch from unequal loading of the bow limbs, slight variations in the nocking point of the arrow on the bow string, and straightness of the arrow shaft. The arrow is also imparted with a bending moment in yaw from torque on the bow handle, skew of the bow limbs, aerodynamic imbalance of the bow string, error in the arrow rest on the bow handle, and also variations in straightness of the arrow. All of these errors exist in every arrow launched, they merely vary in magnitude.
The accuracy of arrow flight is dependent on two primary factors, the foregoing launching errors, and the sensitivity of the arrow to those errors. If the arrow is very flexible it instantaneously curves along its length, so the fletching is simply not pointed in the same direction as the arrowhead. Therefore the arrow must deviate from a straight line of flight. The instantaneous curve of the arrow shaft is constantly changing as the arrow resonates at its characteristic frequency and amplitude, passing through zero flexure where the arrow is perfectly straight, to the opposite direction curve at full amplitude repeatedly, passing through complex and somewhat unpredictable Lassijou figures in a decay time that may be longer than the flight time.
The purpose of this invention is to provide an arrow with an inherently stiff and highly damped structure, having a greatly reduced initial bending amplitude at the moment of launch, and very quickly decaying to zero bending; whereby the arrow shaft remains straight in flight. The inventor has measured flexure amplitudes of as much as .+-.1.0 inch during decay times of over 10 seconds in "high quality" present state-of-the-art arrow shafts, far longer than the vast majority of target or hunting shooting ranges. The inventor then added the prestressing to the same arrow shafts according to the present invention, cutting the amplitude of curvature to less than half that of the unstressed arrow shaft, and also reducing the oscillation decay time to less than two seconds.